Angular Correlation Functions for Models with Logarithmic Oscillations

TL;DR

This paper develops methods to compute angular correlation functions for models with logarithmic oscillations in primordial spectra, revealing their detection challenges and potential observational signatures.

Contribution

It introduces an efficient stationary phase approximation for angular correlations and analyzes the detectability of various logarithmic oscillations in primordial spectra.

Findings

Logarithmic oscillations are mostly featureless in angular correlations

Standard correlators have difficulty detecting these oscillations

Some oscillation types may still be feasible to detect

Abstract

There exist several theoretical motivations for primordial correlation functions (such as the power spectrum) to contain oscillations as a logarithmic function of comoving momentum k. While these features are commonly searched for in k-space, an alternative is to use angular space; that is, search for correlations between the directional vectors of observation. We develop tools to efficiently compute the angular correlations based on a stationary phase approximation and examine several example oscillations in the primordial power spectrum, bispectrum, and trispectrum. We find that logarithmically-periodic oscillations are essentially featureless and therefore difficult to detect using the standard correlator, though others might be feasible.